Hi,
Try to use the same powersupply for both chips. This is the most safe way.
Will it damage the off chip?
It depends on the current. Every datasheet shows the max input current limit. --> look in to the datasheet of the "unpowered chip"
If you are beyond this limit, damage may occur.
But is the other chip able to source that much current? --> look into the datasheet of the "powered chip"
To protect the device you may use current limiting resistors.
Or you may use clamp diodes to VCC.
Or you may use a bus_switch or another chip that is able to withstand HIGH signal input levels wile powed down (like 74AHC / 74AHCT family) as an interface between both chips.
***
The chip can be damaged by
* overcurrent and the generated heat/energy destroys traces
* overvoltage that distroys the isolation barrier
With overcurrent for sure the magnitude of the current as well as the time plays a role.
With overvoltage the isolation barrier may be partly destroyed. This causes increased input currents, mis interpreted input levels, increased power dissipation, total fail of function.
How do then chips tolerate ESD?
The protection diodes keep the voltage low, this ensures that the isolation barrier is safe.
But the ESD energy causes heat. This heat is mainly dissipated in the protection diode...causing heat. If the ESD enrergy is too high, then the diode may be destroyed.
Please review some ESD test conditions. They usually use relatively small capacitors with relatively high series resistance (HBM). Thus most of the previously energy stored in the capacitor is dissipated by the series resistor. It also keeps ESD current low.
I know chips have input protection diode to Vdd so the diode will anyway powerup the off chip but what if there is no diode? What if even with this diode the chip supply is actually tightly pulled by design to keep it off?
You - as the designer - have to take care about this. Choose the correct chips or add protection circuitry.
For example:
* you are free to use a (schottky) diode from one power supply to the other.
* you are free to choose power up sequence.
* you are free to disable the outputs of the "powered chip" when the power of the other device is down.
There are several solutions for the problem - but you have to take care of it.
...when chip has not specified any current limit ...
Any datasheet should give the current limit. Usually in the "Absolute Maximum Ratings" section.
If this value really is not given (which shows the manufacturer didn´t do it´s job) all is guessing. Consider to choose another chip.
Klaus